Optimal Control for Partial Differential Equations of a Heat Exchanger System

Our work is devoted to optimal control of a double-pipe heat exchanger system modeled as coupled hyperbolic partial differential equations (PDEs) of first order in time and space based on adjoint method-calculus of variations, which should be associated with numerical techniques to get solutions. A gradient descent algorithm, which is proved to be convergent after few iterations, is applied to solve the optimal control problem of this heat exchanger (HE) system. Based on the real data in a system, the simulation results demonstrate the effectiveness of the proposed control approach to control the temperatures along the pipes of the HE system, and that the safety of both system and performance is ensured. From these results, we concluded that the gradient descent algorithm is convergent and the method is effective in the optimal control problem of coupled hyperbolic PDEs.